@article { author = {Pandeya, Bashishth and Chaturvedi, Avanish and Gupta, Ashok}, title = {Applications of epi-retractable modules}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {38}, number = {2}, pages = {469-477}, year = {2012}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {An R-module M is called epi-retractable if every submodule of MR is a homomorphic image of M. It is shown that if R is a right perfect ring, then every projective slightly compressible module MR is epi-retractable. If R is a Noetherian ring, then every epi-retractable right R-module has direct sum of uniform submodules. If endomorphism ring of a module MR is von-Neumann regular, then M is semi-simple if and only if M is epi-retractable. If R is a quasi Frobenius ring, then R is a right hereditary ring if and only if every injective right R-module is semi-simple. A ring R is semi-simple if and only if R is right hereditary and every epiretractable right R-module is projective. Moreover, a ring R is semi-simple if and only if R is a pri and von-Neumann regular.}, keywords = {Epi-retractable modules,semi-simple rings,Perfect rings,Hereditary rings,von-Numann regular rings}, url = {http://bims.iranjournals.ir/article_202.html}, eprint = {http://bims.iranjournals.ir/article_202_388757ddee7a3a67ab050c9a998e2049.pdf} }